Explanation:
To solve this question, we can use the formula for the future value of an annuity:
FV = P * (((1 + r)^n - 1) / r)
where:
P is the amount of each deposit (in this case, $400)
r is the interest rate per period (5% / 12 since the interest is compounded monthly)
n is the total number of periods (25 years * 12 months per year = 300 months)
a) Using the formula, we can calculate the future value of the annuity:
FV = 400 * (((1 + 0.05/12)^300 - 1) / (0.05/12)) = $236,463.13
Therefore, you will have $236,463.13 in the account in 25 years.
b) We can calculate the total interest earned on the deposits by subtracting the total amount deposited from the future value of the annuity. The total amount deposited is $400 * 300 months = $120,000, so the total interest earned is:
$236,463.13 - $120,000 = $116,463.13
Therefore, the total interest earned on the deposits is $116,463.13.